The self-similar collapse of three vortices is the motion of three vortices colliding at a single point at finite time. Such a motion has first been shown to exist for two-dimensional, planar, point vortices. In this paper, we show that the concept generalises naturally to three-dimensional quasi-geostrophic vortices as well as to surface quasi-geostrophic vortices. We first determine the conditions

(2020). Correction. Geophysical & Astrophysical Fluid Dynamics. Ahead of Print.

We consider a model for convection in compressible fluids in two dimensions. A constitutive limit is studied in which both the mechanical compressibility and thermal expansion affect the buoyancy force. The motion is no longer isochoric as in the classical Boussinesq approximation but has a uniform expansion rate associated to the upward motion: ∇ ⋅ v = β v z . By using a perturbative approach, we

(2020). Introduction. Geophysical & Astrophysical Fluid Dynamics: Vol. 114, Geophysical and Astrophysical Vortex, pp. 411-413.

The evolution of thin frontal jets in large-scale shallow water quasigeostrophic flow is studied, with a focus on jet curvature and arclength. The flow is large-scale in the sense that mixed regions of potential vorticity (PV) are much larger than the deformation length L D . However the presence of sharp PV fronts with O ( L D ) widths drives the ongoing growth of the flow's length scale; in particular

In the Bay of Biscay (north-east Atlantic), long-living eddies and the frontal activity that they induce substantially contribute to mesoscale and submesoscale dynamics. Tides and river plumes also contribute to frontal activity. Biological productivity is sensitive to river plume fronts and to external forcings (tides and wind). Considering the importance of river plumes, we study here the structure

Clustering of tracers floating on the ocean surface and evolving due to combined velocity fields consisting of a deterministic mesoscale component and a kinematic random component is analysed. The random component represents the influence of submesoscale motions. A theory of exponential clustering in random velocity fields is applied to characterise the obtained clustering scenarios in both steady

We carry out numerical dynamo simulations in a spherical shell to assess the influence of varying Prandtl number on the morphology of the induced magnetic field in both cases when the convection is laminar and turbulent. We work in a regime of large magnetic Prandtl number ( P m = 3 ) due to computational constraints of the full three-dimensional numerical model. We consider dynamos driven by thermal

It is shown that steady large-scale slowly eastward-moving twin-cyclone coherent structures, the equatorial modons, exist in both one- and two layer versions of the rotating shallow water model on the equatorial beta plane. They arise via the process of “ageostrophic adjustment” from the analytic asymptotic modon solutions of the vorticity equation obtained in the limit of small pressure perturbations

We apply Laplace's tidal theory to the evolution of lunar and solar tides on the geologic timescale of Earth's rotation and study the tidal resonance. We study the global tide in the mid-ocean far away from continents. On the short timescale, a linear relationship of tidal height and Earth's rotation is obtained. On the long timescale, the tide is less than 1 metre at present but it was 5 metres in

The vertical profile of the Earth's atmosphere in middle latitudes contains a sharp transition region between two roughly constant stability layers, termed the tropopause and also exhibits jet streams at nearly the same altitude, with the jet stream core possibly above or below the tropopause, depending on time and location. This proximity of the jet to the tropopause would be expected to greatly affect

The present paper describes a combined experimental and high-performance computing study of new specific behaviours of the Strato-Rotational Instability (SRI). The SRI is a purely hydrodynamical instability that consists of a classical Taylor–Couette (TC) system under stable axial density stratification. The density stratification causes a change on the marginal instability transition when compared

We report a new nonlinear phenomenon discovered in the classical problem of thermal convection in a rapidly rotating, self-gravitating, internally heated fluid sphere that also undergoes weak precession. When the Prandtl number of fluids is sufficiently large, convection-driven columnar rolls – which are nearly geostrophic and marked by small azimuthal scale – cannot have substantial nonlinear interaction

The linear equations of thermal convection in a compressible fluid with non-constant transport coefficients are derived. The criterion for the onset of convection is established, based on linear stability analysis, for a range of different temperature-dependent profiles of thermal conductivity and viscosity. Temperature-dependent transport coefficients are shown to lead to a more complex behaviour

We introduce a new high-resolution well-balanced central-upwind scheme for two-dimensional rotating shallow water equations with horizontal temperature/density gradients – thermal rotating shallow water equations. The scheme maintains the equilibrium states in the presence of topography and temperature/density variations, and allows for high-resolution tracking of the active scalar field together with

In this paper, we investigate the vortex–wall interaction on the β-plane, using a submesoscale and internal waves resolving model in an idealised context. Our results bring new insights on the dynamics of oceanic mesoscale eddies as they drift toward a western boundary. We show that there exists a strong cyclone/anticyclone asymmetry in the interaction, contrary to what was suggested in previous studies:

A theoretical problem on linear stationary disturbances introduced by spatial inhomogeneities of gravity field into the background geostrophic flow of the stratified rotating medium (atmosphere) is considered. For the first time, the three-dimensional analytical model is considered. Our results imply that inhomogeneities of the gravity field can lead to ordered perturbations of the velocity field of

Here we examine the motion of an isolated ellipsoidal vortex in a rotating stratified fluid. We derive an analytical solution to a set of balanced equations at the next order to quasi-geostrophic theory, providing insights into geophysical vortices at finite Rossby number ε. This is achieved through the solution of a set of complicated Poisson equations. Though complicated, the analytical solution

Convection and magnetic field generation in the Earth and planetary interiors are driven by both thermal and compositional gradients. In this work numerical simulations of finite-amplitude double-diffusive convection and dynamo action in rapidly rotating spherical shells full of incompressible two-component electrically-conducting fluid are reported. Four distinct regimes of rotating double-diffusive

Several planetary bodies in our solar system undergo a forced libration owing to gravitational interactions with their orbital companions, leading to complex fluid motions in their metallic liquid cores or subsurface oceans. In this study, we numerically investigate flows in longitudinally librating spherical shells. We focus on the Ekman number dependencies of several shear layers when the libration

We examine the equilibrium forms, linear stability and nonlinear evolution of two patches having opposite-signed, uniform potential vorticity anomalies in a single-layer shallow-water flow, under the quasi-geostrophic approximation. We widely vary the vortex area ratio, the potential vorticity anomaly ratio, as well as the Rossby deformation length to unravel the full complexity of possible interactions

Three examples of wave–vortex interaction are studied, in analytically tractable weak refraction regimes with attention to the mean recoil forces, local and remote, that are associated with refractive changes in wave pseudomomentum fluxes. Wave-induced mean forces of this kind can be persistent, with cumulative effects, even in the absence of wave dissipation. In each example, a single wavetrain propagates

Surface ocean currents have a significant influence on the climate and their dynamics depend to a large extent on the behaviour of the vertical eddy viscosity. We present an analytic study of wind-driven surface currents for general depth-dependent vertical eddy viscosities. A novel formulation for Ekman-type flows, that relies of a transformation to polar coordinates, enables us to show that in the

(2020). Correction. Geophysical & Astrophysical Fluid Dynamics: Vol. 114, No. 3, pp. 409-409.

The Red Sea Water enters the Gulf of Aden through the Strait of Bab El Mandeb as a density current. The Red Sea Water subsequently spreads into the Gulf of Aden under the influence of surface mesoscale eddies, which dominate the surface flow, of topographic features such as rift and capes, and of the monsoon regimes. The dynamics of a bottom density current overflowing in a semi-enclosed basin, as

Optimal balance is a near-optimal computational algorithm for nonlinear mode decomposition of geophysical flows into balanced and unbalanced components. It was first proposed as “optimal potential vorticity balance” by Viúdez and Dritschel [J. Fluid Mech., 2004, 521, 343] in the specific setting of semi-Lagrangian potential vorticity-based numerical codes. Later, it was recognised as an instance of

Wave structure interaction problem having thick vertical barrier over an arbitrary seabed is analysed for its solution. The associated boundary value problem is handled using a coupled eigenfunction expansion–boundary element method. This method converts the boundary value problem into integral equation over the physical boundaries. The physical boundaries are discretised into a finite number of elements

Evidence for the emergence of twisted flux tubes into the solar atmosphere has, so far, come from indirect signatures. In this work, we investigate the topological input of twisted flux tube emergence directly by studying helicity and winding fluxes. In magnetohydrodynamic simulations with domains spanning from the top of the convection zone to the lower corona, we simulate the emergence of twisted

(2020). Self-exciting fluid dynamos. Geophysical & Astrophysical Fluid Dynamics. Ahead of Print.

This study is devoted to laboratory experiments on the coalescence of two lenticular anticyclones in a linearly stratified rotating fluid. These anticyclones are generated by injecting small volumes of fluid at the centre of a rotating tank where a linearly stratified layer was previously prepared with salt. The characteristics of the interaction between the vortices are studied by visualisation and

Two common approximations to the full Shallow Water Equations (SWEs) are non-divergence and quasi-geostrophy, and the degree to which these approximations lead to biases in numerical solutions are explored using the test bed of barotropic instability. Specifically, we examine the linear stability of strong polar and equatorial jets and compare the growth rates obtained from the SWEs along with those

Magnetostrophic dynamos are studied in an annular core, adapting the seminal work of Taylor [The magnetohydrodynamics of a rotating fluid and the Earth's dynamo problem. Proc. R. Soc. London A. 1963, 274, 274] for a fluid-filled core. The model consists of an inviscid fluid core and a concentric solid inner core. The fluid is supposed to obey the Boussinesq equations of motion and is driven into motion

Capillary waves are perhaps the simplest example to consider for an introduction to wave turbulence. Since the first paper by Zakharov and Filonenko, capillary wave turbulence has been the subject of many studies, but a didactic derivation of the kinetic equation is still lacking. It is the objective of this paper to present such a derivation in the absence of gravity and in the approximation of deep

We present a series of experimental investigations in which a differentially-heated annulus was used to investigate the effects of topography on rotating, stratified flows. In particular, we investigate blocking effects via azimuthally varying differential-heating and compare them to previous experiments utilising partial mechanical barriers. The thermal topography used consisted of a flat patch of

We study in the linear approximation barotropic Rossby waves in the ocean covered by compressed ice. We derive the dispersion relation and analyse its dependence on the degree of ice compression and its flexural rigidity. The characteristic parameters of a wave-field the most sensible to the influence of ice cover are estimated and presented for the Earth and some other planets. The main conclusion

We analyse the linear stability of filaments of uniform potential vorticity with a horizontal axis in a quasi-geostrophic flow. For a single filament, the situation corresponds to the simplest three-dimensional shear zone in a rapidly rotating, continuously stably stratified fluid. Yet, this has not been formally addressed to our knowledge. We show that the filament is sensitive to the Kelvin–Helmholtz

Laboratory experiments with a rotating cylindrical annulus are reported that reveal a prograde jet, which is adjacent to a (longitudinally) librating inner straight cylindrical wall. Here, wall libration is realised as a time-harmonic modulation of the inner cylinder's rotation rate. The outer cylindrical wall and bottom and top lids rotate with constant angular velocity. The main purpose of our study

The Red Sea Water is a warm and salty water produced in the Red Sea by evaporation induced by strong solar radiation. This dense water mass exits the Red Sea through the Strait of Bab El Mandeb, and enters the Gulf of Aden as a density current between 400 and 1000 metre depth. In the Gulf of Aden, in situ and satellites observations have shown the impact of the deeply reaching eddies dominating the

(2020). Introduction. Geophysical & Astrophysical Fluid Dynamics: Vol. 114, On the Physics and Algorithms of the Pencil Code, pp. 1-7.

Atmospheric water has a complex behaviour partly due to the influence of precipitation. Consequently, it is challenging to explain properties of water such as the scale-dependence of its variance, for which a range of spectral exponents has been identified in observational data. Here, a precipitating quasi-geostrophic (PQG) model is explored as a possible prototype for contributing to understanding

Atmospheres of gas-giant planets are driven by thermal convection and often exhibit cyclonic circulation at the poles. Here we present the results of the numerical simulations of individual cold and warm blobs in a polar area of a rotating deep spherical layer. The simulations show that the cyclones created at the top of the atmosphere by sinking cold blobs translate northward. The cyclones are the

Geometric stability theory is developed as an analogue of structural stability in physical space. Two steady flows are said to be geometrically equivalent if they have the same streamline pattern with velocities satisfying uˆ=F(x,y,z)u. A stationary solution to the Euler equations is non-unique if there exists a geometrically equivalent solution with horizontally varying F, in which case its geometric

Oil wells contain two-phase liquid and gas mixtures driven upwards due to a pressure gradient. In this paper, we study a two-fluid model for vertical upwelling flow and explicitly account for the exsolution of the dissolved gas as the pressure decreases along the well. We find that the application of Henry's law for the dissolved gas concentration predicts a rapid transition to a foam, which runs counter

We present a radiative magneto-hydrodynamic simulation set-up using the pencil code to study the generation, propagation and dissipation of Alfvén waves in the solar atmosphere which includes a convective layer, photosphere below and chromosphere, transition region and the corona above. We prepare a set-up of steady-state solar convection where the imposed external magnetic field also has reached the

ABSTRACT Explicit radiation hydrodynamic simulations of the atmospheres of massive stars and of convection in accretion discs around white dwarfs suffer from prohibitively short time steps due to radiation. This constraint is related to the cooling time rather than the radiative pressure, which also becomes important in hot stars and discs. We show that the radiative time step constraint is governed

Stably stratified layers are present in stellar interiors (radiative zones) as well as planetary interiors – recent observations and theoretical studies of the Earth's magnetic field seem to indicate the presence of a thin, stably stratified layer at the top of the liquid outer core. We present direct numerical simulations of this region, which is modelled as an axisymmetric spherical Couette flow

ABSTRACT The hot loop structures in the solar corona can be well modelled by three-dimensional magnetohydrodynamic simulations, where the corona is heated by field line braiding driven at the photosphere. To be able to reproduce the emission comparable to observations, one has to use realistic values for the Spitzer heat conductivity, which puts a large constraint on the time step of these simulations

ABSTRACT We present a high-resolution convergence study of detonation initiated by a temperature gradient in a stoichiometric hydrogen–oxygen mixture using the PENCIL CODE and compare with a code that employs a fifth order weighted essentially non-oscillating (WENO) scheme. With Mach numbers reaching 10–30, a certain amount of shock viscosity is needed in the PENCIL CODE to remove or reduce numerical

(2020). Correction. Geophysical & Astrophysical Fluid Dynamics: Vol. 114, No. 3, pp. 410-410.

We consider the interaction between two quasi-geostrophic vortices of height-to-width aspect ratio h/r, lying at two different vertical levels. We investigate whether such structures naturally align. In the case the vortices occupy distinct yet contiguous vertical levels, such an alignment can contribute to the growth in volume of oceanic mesoscale vortices. The other growth mechanism is the merger

ABSTRACT Recent numerical work in helioseismology has shown that a periodically varying subsurface magnetic field leads to a fanning of the f-mode, which emerges from a density jump at the surface. In an attempt to model a more realistic situation, we now modulate this periodic variation with an envelope, giving thus more emphasis on localised bipolar magnetic structures in the middle of the domain

Hydromagnetic turbulence produced during phase transitions in the early universe can be a powerful source of stochastic gravitational waves (GWs). GWs can be modelled by the linearised spatial part of the Einstein equations sourced by the Reynolds and Maxwell stresses. We have implemented two different GW solvers into the Pencil Code – a code which uses a third order timestep and sixth order finite

The quality of today's research is often tightly limited to the available computing power and scalability of codes to many processors. For example, tackling the problem of heating the solar corona requires a most realistic description of the plasma dynamics and the magnetic field. Numerically solving such a magneto-hydrodynamical (MHD) description of a small active region (AR) on the Sun requires millions

High Mach number shocks are ubiquitous in interstellar turbulence. The Pencil Code is particularly well suited to the study of magnetohydrodynamics in weakly compressible turbulence and the numerical investigation of dynamos because of its high-order advection and time evolution algorithms. However, the high-order algorithms and lack of Riemann solver to follow shocks make it less well suited to handling

The chiral magnetic effect (CME) is a quantum relativistic effect that describes the appearance of an additional electric current along a magnetic field. It is caused by an asymmetry between the number densities of left- and right-handed fermions, which can be maintained at high energies when the chirality flipping rate can be neglected, for example in the early Universe. The inclusion of the CME in

We test the sensitivity of hydrodynamic and magnetohydrodynamic turbulent convection simulations with respect to Mach number, thermal and magnetic boundary conditions, and the centrifugal force. We find that varying the luminosity, which also controls the Mach number, has only a minor effect on the large-scale dynamics. A similar conclusion can also be drawn from the comparison of two formulations

Two methods for solid body representation in flow simulations available in the Pencil Code are the immersed boundary method and overset grids. These methods are quite different in terms of computational cost, flexibility and numerical accuracy. We present here an investigation of the use of the different methods with the purpose of assessing their strengths and weaknesses. At present, the overset grid